What makes a cosmic filament? The dynamical origin and identity of filaments – I. Fundamentals in 2D

Cosmic filaments are the transport channels of matter in the Megaparsec Universe, and represent the most prominent structural feature in the matter and galaxy distribution. Here, we describe and define the dynamical nature of cosmic filaments, based on the realization that the complex spatial pattern and connectivity of the cosmic web are already visible in the primordial random density field, in the spatial pattern of the primordial tidal and deformation eigenvalue field. The filaments emerging from this are multistream features and structural singularities in phase-space. The caustic skeleton formalism allows a fully analytical classification, identification, and treatment of the nonlinear cosmic web. The caustic conditions yield the mathematical specification of web-like structures in terms of the primordial deformation tensor eigenvalue and eigenvector fields, in which filaments are identified – in two dimensions – with the so-called cusp caustics. These are centred around points that are maximally stretched. The resulting mathematical conditions represent a complete characterization of filaments in terms of their formation history, dynamics, and orientation. We illustrate the workings of the formalism based on a set of constrained N-body simulations of proto-filament realizations. These realizations are analysed in terms of spatial structure, density profiles, and multistream structure and compared to simpler density or potential field saddle point specifications. The presented formalism, and its three-dimensional generalization, will facilitate the mining of the rich cosmological information contained in the observed web-like galaxy distribution, and be of key significance for the analysis of cosmological surveys such as Sloan Digital Sky Survey, Dark Energy Spectroscopic Instrument (DESI), and Euclid.